Question

The hypotenuse of a right triangle is 13ft long. The longer leg is 7ft longer than the shorter leg. Find the side lengths of the triangle.

Answer 1

Answer:

The short side is 5ft and the longer side 12ft

Step-by-step explanation:

I knew that the hypotenuse was 13 so it couldn’t be more than 13. I was guessing at numbers until I got to 5 then added 7. After I use Pythagorean theorem to check and I got 13.

Answer 2

Answer:

The side lengths are 5, 12, 13

Step-by-step explanation:

These are the side lengths we know before we have solved the problem.

a= x   b= x+7   c= 13

If we put this into the Pythagorean theorem, we get

$13^{2} = x^{2} +(x+7)^{2}$

Expand

$169 = 2x^2+14x+49$

Subtract 169 from both sides

$0 =2x^2+14x-120$

Solve using the quadratic formula

a= 2   b= 14   c= -120

$\frac{-14\pm \sqrt{14^2-4\cdot \:2\left(-120\right)}}{2\cdot \:2}$

$x= \frac{-14\pm \:34}{2\cdot \:2}$  

If we separate the solutions we get

$x= \frac{20}{4} = 5$

and

$x= \frac{-48}{4} = -12$

Since this is a question about length, we can ignore the negative.

So the longer leg is 12ft and the shorter leg is 5ft